(Invert a triangular map)
Given a map \(S\)  of the form
(REF ) and an
\(x\in \mathbb {R}^n\) ,
solve the
nonlinear system
\(S(z) = x\)  for
\(z\) .


[1]
InvertMap S, \(x\)  \(k\leftarrow 1\)  to \(n\) 
\(z_k \leftarrow \)  Solve
\(S^k(z_1,\ldots ,z_{k-1}, \xi ) = x_k\) 
for \(\xi \in \mathbb {R}\) 
one-dimensional root finding [1]}
\({z= (z_1,\ldots ,z_n)}\)
